Step 1 :First, we can find the value of $y$ by multiplying the first equation by $3$ and the second equation by $2$ and then subtracting the first equation from the second equation.
Step 2 :\(6y-21z=-51\)
Step 3 :\(6y-22z=-54\)
Step 4 :Subtracting the first equation from the second equation, we get:
Step 5 :\(z=3\)
Step 6 :Now, we can substitute the value of $z$ into the first equation to find the value of $y$:
Step 7 :\(2y-7(3)=-17\)
Step 8 :\(2y-21=-17\)
Step 9 :\(2y=4\)
Step 10 :\(y=2\)
Step 11 :Thus, our answer is \(\boxed{(2,3)}\)